six degrees of danish bacon
The current issue of New Left Review has an article by Franco Moretti applying a bit of network analysis to the interactions within some pieces of literature. Here is the interaction network in Hamlet, with a tie being defined by whether the characters speak to one another. (Notice that this means that, e.g., Rosencrantz and Guildenstern do not have a tie, even though they’re in the same scenes.)
And here is Hamlet without Hamlet:
I think we can safely say that he is a key figure in the network. Though the Prince may be less crucial than he thinks, as Horatio seems to be pretty well positioned, too. Lots more in the article itself.